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Testing for a Linear Unit Root against Nonlinear Threshold Stationarity




In this paper we propose a direct testing procedure to detect the presence of linear unit root against geometrically ergodic process defined by the self-exciting threshold autoregressive (SETAR) model with three regimes. Assuming that the process follows the random walk in the corridor regime, the null can be tested by the Wald test for the joint significance of the threshold autoregressive parameters under both lower and upper regimes. We prove that the suggested Wald test does not depend on unknown threshold values under the null at least asymptotically. We also derive its analytic asymptotic null distribution. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the standard Dickey-Fuller test that ignores the threshold nature under the alternative.

Suggested Citation

  • George Kapetanios & Yongcheol Shin, 2000. "Testing for a Linear Unit Root against Nonlinear Threshold Stationarity," ESE Discussion Papers 60, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:60

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    Cited by:

    1. Laurence Copeland & Saeed Heravi, 2009. "Structural breaks in the real exchange rate adjustment mechanism," Applied Financial Economics, Taylor & Francis Journals, vol. 19(2), pages 121-134.

    More about this item


    self-exciting threshold autogressive model; exponentially ergodic process; unit roots; thresholds cointegration; Wald tests; critical values; Monte Carlo simulations;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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